Banks and rival lenders are butting heads over the credit scores used to decide millions of mortgage requests by U.S. home buyers.

Now, a federal agency is weighing whether to step into the fight, which revolves around a longtime requirement for lenders who sell mortgages to Fannie Mae and Freddie Mac to gauge most borrowers using FICO scores. The Federal Housing Finance Agency’s ultimate decision could have wide-reaching ramifications for the mortgage market and home buyers across the U.S.